I am being given a data set that includes approximately 12,000 individuals. There are two cohorts, however one cohort (N=4873) has two waves and the second cohort (N=8579) has three waves of data. More specifically, both cohorts have data at age 16. One cohort has data at age at the second wave. Both cohorts have data at the third wave. Thus, it is as if there were a single cohort (N=13452), with a third of individuals missing data at the second wave. The reviewers are asking for a longitudinal analysis, perhaps an LGM or LCGA? Do you have any recommendations for dealing with this data set? The dependednt variable is smoking (yes/no) at each wave. The independent variables are all binary (e.g., maternal smoking at baseline).

You can do LGM or LCGA using either a single-group analysis allowing missing data as you indicate or using a 2-group analysis of the two cohorts, testing that they come from the same population. The former approach might be simpler here.

I am also using cohort sequential design to obtain age-based measurements to look at constructs across age 12 to 22...however, each individual was only observed 3 times. I tried to examine a quadratic trajectory, but Mplus would only allow linear. Just wanted to make sure that this was as it should be given that I have only 3 time points per case.

You can use the cohort approach of UG ex 6.18. Because you are using mixtures, you will have to replace Grouping with Knownclass. This means that you have one Knownclass "cg" latent class variable and one regular "c" latent class variable much like in UG ex8.8.